( (product of adjacent risk magnitudes)), where is a constant depending on the number of risk dimensions. Then, assuming { [ (product of adjacent risk magnitudes)]} is a constant at one point in time we can represent this signature as a constant, beta ( ). These changes are therefore observed to be almost zero over time for any particular ITO exercise. This is also demonstrated in the case study exercise in Chapter 8, and is observed to apply to the buyer organization and its total risk exposure profile over time.
State of equilibrium
When both the buyer and supplier are considered together and assuming a natural state where (buyer) (supplier), then the objective is to achieve a situation of equilibrium where the risks are described mathematically as
(buyer). dt (supplier). dt 0
∫
∫
0
0
over time, for both the supplier and buyer organizations. Any fluctuations in risk exposure for (buyer) should, through negotiations, control and governance, be also reflected for
(supplier). The use of the infinite limit is for illustrative purposes only, i.e. to show that over time the buyer and supplier would reach agreements that determine equity for both sides.
In summary, the equation describes a situation over a significant amount of time, when the buyer and the supplier profiles would be the same. In an RDS, there are an infinite number of variables that need to be accounted for; also risks are not forces of nature but a humanly derived concept. The concept of a state 147
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of equilibrium also exists when the RDS is perfectly octagonal (for eight risk dimensions). This is the state where the risk exposure in all the dimensions is the same and there is no further need to trade one risk off against another. The magnitude of the risk exposure, i.e. the area bounded by the octagonal RDS profile, then needs to be reduced.
By way of comparison, the analogy of the lever, where the magnitude of the force and distance away from the fulcrum can be controlled, can be applied to both the risk exposure ( ) signature, and time ( t), through an understanding of the relationships between risk dimensions. The fact that the two equations involved simplify to two controllable variables is completely coinciden-tal. The main assumption, however, is that the variables can be controlled via the manipulation of events, actions or activities.
The RDS profiles in this chapter can be extended to show the risk balancing phenomenon which was observed during the exercise.
Risk balancing occurs when several events are made to occur in order to mitigate the risks along one of the risk dimensions, which affects other risk dimensions to the extent that an almost perfect octagon is achieved. By way of analogy, this is much like a see-saw where there is a relationship between the load and distance from the fulcrum where Work (W) Load (L) Distance (D) from the fulcrum (Figure 6.3). This is a simplistic example where the see-saw will come to rest in a horizontal state when W1 and W2 are equal.
The analogy ends where there are a finite number of variables in the equation for the lever; moreover the lever is governed by the laws of motion. This is, however, consistent with the observations made during this exercise. Each time the risk factors and risk exposure are high (indicated by a spike in the RDS), the risks from another risk dimension can be used to reduce the first dimension. The case study (see Chapter 8) describes a suitable environment to observe this phenomenon. It has been shown W1 L1 D1
W2 L2 D2
L2
L1
Figure 6.3
The lever and forces
D1
D2
in equilibrium
148
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Risk Characteristics and Behaviour in an ITO Exercise that there is a direct and immediate relationship between the risk dimensions to the extent that the risk exposures along each of them compensate for the increase or reduction in the others until the total risk exposure for the organization’s ITO exercise reverts to the original value.
There is a period over which the total risk exposure appears constant. There is also a period, which could be many times longer, when the total risk exposure for both the supplier and the buyer is the same. Two major areas where the new understanding of these characteristics of risk dimensions could be helpful include the determination of strategies to shape the risk profile to within an organization’s tolerance limits, and the optimal duration of ITO contracts.
6.6
Game theory
Game theory is another perspective that can be used to describe conditions in which different types of organizational arrangements develop and change. It involves the interaction between individuals or organizations. McMillan (1992) mentions that game theory ‘is a study of rational behaviour in situations involving interdependence’. The notion of equilibrium and a state of constancy observed in the scenarios in this chapter are arguably closely coupled with game theory.
Game theory is not concerned with defining objectives, design-ing the alternatives or assessing the consequences where these are considered as being of external derivation or previously determined from the RDS data. It offers two main approaches. The first exploits criteria of choice developed in a broader context by game theory, as for example the max–min rule, where we choose the alternative such that the worst possible consequence of the chosen alternative is better than (or equal to) the best possible consequence of any other alternative. The second approach is to reduce the uncertainty in the case of risk by using subjective probabilities, based on expert assessments or on analysis of previous decisions made in similar circumstances. With information from the RDS and relationships between each risk dimension, the alternative actions by the team will have one of several possible consequences. The probability of occurrence for each consequence can be computed and hence each alternative can be associated with a probability distribution. The decision-makers hence can make choices among probability distributions. When the probability distributions are unknown, one speaks about decision under uncertainty. Game theory then ranks the possible 149
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decisions using a set of criteria consistent with the decision-maker’s objectives and preferences.
The payoffs for the variety of situations that occur between the buyer and supplier also represent various conflicts. In this situation, gains and losses may be unequally distributed, which allows the representation of numerous competitive and conflict situations. Game theory then proposes several solutions, e.g. in a min–max strategy each of the participants minimizes the maximum loss the other can impose on him; a mixed strategy involves probabilistic choices. Experiments with such games revealed conditions for co-operation, defection and the persist-ence of conflict. If we combine this scenario with the theory postulated earlier, i.e. that the total risk exposure is in a state of constancy throughout the exercise where the dynamics of the risks along each risk dimension compensate for one another in the course of the exercise, then there is a state where there is an equilibrium to be reached. There is no overriding winning strategy that either the buyer or the supplier needs to make.
When the observations and theories proposed in the previous sections are compared with the component parts of game theory, then the connection is not as far fetched as it may initially appear.
It lies very much in the interaction between the supplier and the buyer organizations which, in turn, determine and influence the risk profiles. This was used in the context of formulating a tool for the understanding of information services outsourcing (Elitzur and Wensley, 1997). A situation in game theory arises where the Nash equilibrium is observed (Nash, 1951; 1953). A Nash equilibrium situation arises where a set of strategies of all players in a game exists when no player has incentive to deviate from his strategy given that the other players do not deviate. The mathematical principles of game theory involve an analysis of interactions among various economic players. This is highlighted here for comparative purposes in relation to the ITO exercise.
The point needs to be raised that a situation might develop in which the total risk exposure remains constant despite the changes in the risk profile. This supports the argument where the strategies of both the supplier and the buyer also reach equilibrium with knowledge of this state. This concept can be explored further to include the ability and interaction of the parties – buyer and supplier – to influence the RDS. In his paper, Nash focused on rivalries in which all players could benefit, showing that there were solutions to game theory problems in which no player would be able to do better than any other player, even if 150
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Risk Characteristics and Behaviour in an ITO Exercise one player knew what the other players were doing. Nash distinguished between co-operative games, in which binding agreements are made, and non co-operative games, in which binding agreements are not feasible. The Nash equilibrium appears appropriate in the context of this discussion as it provides further explanation for equilibrium in the risk profiles. This situation also involves two (or more) players over a period of time, and in constant negotiation with each other, allowing the application of Nash’s theory.